Question

rich is attending a 4-year college. as a freshman, he was approved for a 10-year, federal unsubsidized student loan in the amount of $7,900 at 4.29%. he knows he has the option of beginning repayment of the loan in 4.5 years. he also knows that during this non - payment time, interest will accrue at 4.29%. suppose rich only paid the interest during his 4 years in school and the six - month grace period. what will he now pay in interest over the term of his loan? note: please make sure to properly format your answers. all dollar figures in the answers need to include the dollar sign and any amount over 1,000 should include the comma ($2,354.67). all percentage values in the answers need to include a percentage sign (%), for all items without specific rounding instructions, round your answers to two decimal places, show both decimal places (5.06).

Explanation:

Step1: Determine the total time for interest accrual

Rich is in school for 4 years and has a 6 - month (0.5 years) grace period. So the total time \( t \) is \( 4 + 0.5=4.5 \) years.

Step2: Use the simple interest formula \( I = Prt \)

The principal \( P=\$47900 \), the annual interest rate \( r = 4.29\%=0.0429 \), and time \( t = 4.5 \) years.
Substitute the values into the formula: \( I=47900\times0.0429\times4.5 \)

First, calculate \( 47900\times0.0429 \):
\( 47900\times0.0429 = 47900\times\frac{429}{10000}=\frac{47900\times429}{10000}=\frac{20549100}{10000} = 2054.91\)

Then, multiply by \( 4.5 \):
\( 2054.91\times4.5=2054.91\times\frac{9}{2}=\frac{2054.91\times9}{2}=\frac{18494.19}{2} = 9247.095\approx9247.10\)

Answer:

\$9,247.10